Example 92.1 Using Summary Statistics to Compare Group Means

This example, taken from Huntsberger and Billingsley (1989), compares two grazing methods using 32 steers. Half of the steers are allowed to graze continuously while the other half are subjected to controlled grazing time. The researchers want to know if these two grazing methods affect weight gain differently. The data are read by the following DATA step:

The variable GrazeType denotes the grazing method: "controlled" is controlled grazing and "continuous" is continuous grazing. The dollar sign ($) following GrazeType makes it a character variable, and the trailing at signs (@@) tell the procedure that there is more than one observation per line.

If you have summary data—that is, just means and standard deviations, as computed by PROC MEANS—then you can still use PROC TTEST to perform a simple test analysis. This example demonstrates this mode of input for PROC TTEST. Note, however, that graphics are unavailable when summary statistics are used as input.

The MEANS procedure is invoked to create a data set of summary statistics with the following statements:

The NOPRINT option eliminates all printed output from the MEANS procedure. The VAR statement tells PROC MEANS to compute summary statistics for the WtGain variable, and the BY statement requests a separate set of summary statistics for each level of GrazeType. The OUTPUT OUT= statement tells PROC MEANS to put the summary statistics into a data set called newgraze so that it can be used in subsequent procedures. This new data set is displayed in Output 92.1.1 by using PROC PRINT as follows:

proc print data=newgraze;
run;

The _STAT_ variable contains the names of the statistics, and the GrazeType variable indicates which group the statistic is from.

Output 92.1.1
Output Data Set of Summary Statistics

Obs

GrazeType

_TYPE_

_FREQ_

_STAT_

WtGain

1

continuous

0

16

N

16.000

2

continuous

0

16

MIN

12.000

3

continuous

0

16

MAX

130.000

4

continuous

0

16

MEAN

75.188

5

continuous

0

16

STD

33.812

6

controlled

0

16

N

16.000

7

controlled

0

16

MIN

28.000

8

controlled

0

16

MAX

128.000

9

controlled

0

16

MEAN

83.125

10

controlled

0

16

STD

30.535

The following statements invoke PROC TTEST with the newgraze data set, as denoted by the DATA= option:

proc ttest data=newgraze;
class GrazeType;
var WtGain;
run;

The CLASS statement contains the variable that distinguishes between the groups being compared, in this case GrazeType. The summary statistics and confidence intervals are displayed first, as shown in Output 92.1.2.

Output 92.1.2
Summary Statistics and Confidence Limits

The TTEST Procedure

Variable: WtGain

GrazeType

N

Mean

Std Dev

Std Err

Minimum

Maximum

continuous

16

75.1875

33.8117

8.4529

12.0000

130.0

controlled

16

83.1250

30.5350

7.6337

28.0000

128.0

Diff (1-2)

-7.9375

32.2150

11.3897

GrazeType

Method

Mean

95% CL Mean

Std Dev

95% CL Std Dev

continuous

75.1875

57.1705

93.2045

33.8117

.

.

controlled

83.1250

66.8541

99.3959

30.5350

.

.

Diff (1-2)

Pooled

-7.9375

-31.1984

15.3234

32.2150

25.7434

43.0609

Diff (1-2)

Satterthwaite

-7.9375

-31.2085

15.3335

In Output 92.1.2, The GrazeType column specifies the group for which the statistics are computed. For each class, the sample size, mean, standard deviation and standard error, and maximum and minimum values are displayed. The confidence bounds for the mean are also displayed; however, since summary statistics are used as input, the confidence bounds for the standard deviation of the groups are not calculated.

Output 92.1.3 shows the results of tests for equal group means and equal variances.

Output 92.1.3
t Tests

Method

Variances

DF

t Value

Pr > |t|

Pooled

Equal

30

-0.70

0.4912

Satterthwaite

Unequal

29.694

-0.70

0.4913

Equality of Variances

Method

Num DF

Den DF

F Value

Pr > F

Folded F

15

15

1.23

0.6981

A group test statistic for the equality of means is reported for both equal and unequal variances. Both tests indicate a lack of evidence for a significant difference between grazing methods ( and for the pooled test, and for the Satterthwaite test). The equality of variances test does not indicate a significant difference in the two variances . Note that this test assumes that the observations in both data sets are normally distributed; this assumption can be checked in PROC UNIVARIATE by using the NORMAL option with the raw data.

Although the ability to use summary statistics as input is useful if you lack access to the original data, some of the output that would otherwise be produced in an analysis on the original data is unavailable. There are also limitations on the designs and distributional assumptions that can be used with summary statistics as input. For more information, see the section Input Data Set of Statistics.